Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models

该项目涉及开发创新的富Galerkin方法，以可靠地模拟压力驱动裂缝问题。在此范围内，该项目将考虑在（准）不可压缩材料中进行准静态和动态裂缝扩展的压力驱动裂缝的声音建模。重点将给予不可压缩极限的分析，结合混合公式和最近的压力鲁棒离散的斯托克斯方程。这将通过设计基于与断裂不可逆性相关的变分不等式的新的有效误差估计的收敛自适应网格细化方案来补充。

The project is concerned with the development of innovative enriched Galerkin methods for the reliable simulation of pressure-driven fracture problems.Within this scope the project will consider the sound modeling of pressure driven fractures in (quasi-)incompressible materials for quasi-static and dynamic fracture-propagation. Emphasis will be given to the analysis of the incompressible limit by combining mixed formulations together with recent pressure robust discretizations for the Stokes-equation.This will be complemented by designing convergent adaptive mesh-refinement schemes based on new efficient error estimators for the variational inequality associated with the fracture irreversibility.